Forward error correction scheme for CDMA data channels using universal turbo codes

ABSTRACT

A method of providing forward error correction for data services uses a parallel concatenated convolutional code which is a Turbo Code comprising a plurality of eight-state constituent encoders wherein a plurality of data block sizes are used in conjunction with said Turbo Code. A variation uses the method in a cellular radio system. Another variation uses the method in both forward and reverse likes of a cellular radio system.

CLAIM FOR PRIORITY

[0001] This application claims priority under 35 U.S.C. § 1.119(e) ofthe filing dates of U.S. Provisional Application Nos. 60/072,368, filedJan. 23, 1998, 60/074,932, filed Feb. 17, 1998, 60/075,742, filed Feb.23, 1998, and 60/076,464, filed Mar. 2, 1998.

BACKGROUND OF THE INVENTION

[0002] The present invention relates to error correction in datacommunications, and more particularly, to forward error correction(FEC). Even more particularly, the present invention relates theselection and use of optimal Turbo Codes in high performance datacommunication systems, such as emerging third generation terrestrialcellular mobile radio and satellite telephone systems, for whichflexibility in supporting a wide range of system requirements withrespect to transmission data rates, channel coding rates, quality ofservice measures (e.g., latency, bit-error rate, frame error rate), andimplementation complexity are highly desirable.

[0003] Forward error correction (FEC) is required in terrestrial andsatellite radio systems to provide high quality communication over theRF propagation channel, which induces signal waveform and spectrumdistortions, including signal attenuation (freespace propagation loss)and multi-path induced fading. These impairments drive the design of theradio transmission and receiver equipment, the design objective of whichis to select modulation formats, error control schemes, demodulation anddecoding techniques and hardware components that together provide anefficient balance between system performance and implementationcomplexity. Differences in propagation channel characteristics, such asbetween terrestrial and satellite communication channels, naturallyresult in significantly different system designs. Likewise, existingcommunication systems continue to evolve in order to satisfy increasedsystem requirements for new higher rate or higher fidelity communicationservices.

[0004] In the case of terrestrial cellular mobile radio telephony,Analog Mobile Phone System (AMPS) is an exemplary first generationsystem; the U.S. IS-136 and European GSM time-division multiple-access(TDMA) standards and the U.S. IS-95 code-division multiple-access (CDMA)standard are second generation systems; and the wideband CDMA standardscurrently under development (e.g., CDMA 2000 in the U.S. and UTRA inEurope) are third generation systems.

[0005] In the third generation systems the development of flexible,high-speed data communication services is of particular interest.Desirable features include the ability to perform rate adaptation and tosatisfy a multiplicity of quality-of-service (QoS) requirements.

[0006] Traditional forward error correction (FEC) schemes forcommunication systems include use of convolutional codes, block codessuch as Reed-Solomon or BCH codes, and/or concatenated coding schemes.

[0007] Turbo Codes are a relatively new class of block codes that havebeen demonstrated to yield bit error rate (BER) performance close totheoretical limits on important classes of idealized channels by meansof an iterative soft-decision decoding method.

[0008] A Turbo encoder consists of a parallel concatenation of typicallytwo systematic, recursive convolutional codes (“constituent codes”)separated by an interleaver that randomizes the order of presentation ofinformation bits to the second constituent encoder with respect to thefirst constituent encoder. The performance of a Turbo Code depends onthe choice of constituent codes, interleaver, information block size(which generally increase with higher data rates), and number of decoderiterations. For a particular Turbo Code, in which the constituent codesare fixed, one can ideally adjust the block size and number of decoderiterations to trade-off performance, latency, and implementationcomplexity requirements. As the block size changes, however, a newinterleaver matched to that block size is required.

[0009] In a CDMA network with synchronized base stations, the forwardlink channels (from base station to user terminal) can be designed to beorthogonal, using, for example, Walsh-Hadamard spreading sequences. Thisis generally not possible, however, for reverse link channels (from userterminal to base station), which therefore operate asynchronously usingspreading sequences that are only quasi-orthogonal. Thus, the reverselinks in a synchronous CDMA network typically experience moreinterference and therefore may require stronger FEC (via lower ratecodes) than the forward link channels do.

[0010] In an asynchronous CDMA network, the forward and reverse linkchannels are more similar in terms of interference levels, so it ispossible to use a common FEC scheme (or at least more similar FECschemes) on the two links.

[0011] The flexibility and high performance of Turbo Codes make them apotentially attractive technology for sophisticated data communicationsservices. It is therefore desirable to identif Turbo Codes and Turbocoding FEC schemes that best match diverse service requirements withrespect to data rates and coding rates while minimizing implementationcomplexity.

[0012] The present invention advantageously addresses the above andother needs by providing methods for designing and using universallyoptimized Turbo Codes.

SUMMARY OF THE INVENTION

[0013] The present invention advantageously addresses the needs above aswell as other needs by providing an approach for designing universalconstituent codes of Turbo Codes providing optimal performance inconjunction with a variety of different interleaver depths and TurboCode rates.

[0014] The present invention is characterized, in its most basic form asa method of providing forward error correction for data services using aparallel concatenated convolutional code (PCCC) which is a Turbo Codecomprising of a plurality of eight-state constituent encoders wherein aplurality of data block sizes are used in conjunction with said TurboCode.

[0015] In one variation, the method of forward error correction furtheruses a universal Turbo Code in a cellular mobile radio system.

[0016] In one embodiment, the method of forward error correction furtheruses a universal Turbo Code in a forward link and a reverse link of acellular mobile radio system.

[0017] Specific universal Turbo Codes, with sets of optimized puncturingpatterns capable of providing several commonly used code rates, areidentified that provide uniformly near-optimal bit error rate and frameerror rate performance over a wide range of information block sizes(hence, data rates) for a set of supported code rates.

[0018] Several universal Turbo Codes are identified herein and differfrom each other in terms of: 1) the targeted code rate for which thechoice of constituent encoders is optimized; and 2) flexibility withregard to the lowest code rate supported.

[0019] A suite of preferred universal Turbo Codes is provided from whicha Turbo Coding FEC scheme is crafted to best meet the specific designrequirements of a sophisticated data communication system.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The above and other aspects, features and advantages of thepresent invention will be more apparent from the following moreparticular description thereof, presented in conjunction with thefollowing drawings wherein:

[0021]FIG. 1 is a diagram of a CDMA digital cellular mobile radio systemhardware;

[0022]FIG. 2 is a diagram of a CDMA digital cellular mobile radio systemhardware which can implement an embodiment of the present invention;

[0023]FIG. 3 is a functional block diagram of a Turbo Code encodermodified for use with the present invention;

[0024]FIG. 4 is a functional block diagram of a Turbo Code decoder;

[0025]FIGS. 5, 6, 7, 8 illustrate the Bit Error Rate (BER) performanceagainst signal-to-noise ratio (SNR) for Turbo Code rate ½ and rate ⅓ atInterleaver sizes 1000, 512, and 1024 bits when the Turbo Codes use acandidate constituent code represented by d(D), and n(D);

[0026]FIG. 9 illustrates the puncturing schemes studied for optimizingthe rate ¼ Turbo Codes;

[0027]FIGS. 10, 11, 12 illustrate the BER/FER performance of ConstituentCodes #1-3 at a frame size of 512 bits;

[0028]FIG. 13 illustrates the BER/FER performance of Constituent Code#1, wherein Constituent Code #1 is at a frame size of 1024 bits, andwith consistent results found at sizes 2048 and 3072 bits, respectively;

[0029]FIG. 14 illustrates the BER/FER performance of selected rate ¼Turbo Codes at frame size 512 bits, with consistent results found atsizes 1024, 2048, and 3072 bits, respectively;

[0030]FIG. 15 is a comparison of preferred Turbo Code B against otherpuncturing schemes at frame size 512 bits;

[0031]FIG. 16 is a lay-out of candidate puncturing patterns for TurboCodes of rate ⅓ and rate ½ when the constituent codes have rate ⅓;

[0032]FIG. 17 illustrates a comparison of rate ⅓ puncturing schemes atframe size 512 bits;

[0033]FIG. 18 illustrates rate ½ puncturing schemes at frame size 512bits, with consistent results found at 1024, 2048, and 3072 bits,respectively;

[0034]FIG. 19 illustrates a block diagram of a preferred universalconstituent encoder for Turbo Codes optimized at code rate ½ and rate ⅓of varying Interleaver depths;

[0035]FIG. 20 is a functional block diagram for rate ¼ Turbo Codesoptimized at code rate ½ and rate ⅓, including interleaving andpuncturing, (rate ⅓, and rate ½ use analogous processing);

[0036]FIG. 21 illustrates puncturing patterns for rate ⅜ Turbo Codes;

[0037]FIG. 22 illustrates rate ⅜ Turbo Codes optimized at code rate ½and rate ⅓ at frame size 512 bits, wherein results are consistent at1024, 2048, and 3072 bits, respectively;

[0038]FIG. 23 illustrates puncturing patterns for rate {fraction (4/9)}Turbo Codes;

[0039]FIG. 24 illustrates rate {fraction (4/9)} Turbo Codes optimized atcode rate ½ and rate ⅓ using frame size 512 bits;

[0040]FIG. 25 is a functional block diagram of a preferred constituentencoder for Turbo Codes optimized at code rate ¼;

[0041]FIG. 26 illustrates a functional block diagram of a rate ¼ TurboCodes optimized at rate ¼ including interleaving and puncturing, (rate ⅓and rate ½ use analogous processing);

[0042]FIG. 27 illustrates puncturing patterns for rate {fraction (2/9)}Turbo Codes;

[0043]FIG. 28 illustrates rate {fraction (2/9)} Turbo Codes optimized atcode rate ¼ using frame size 512 bits;

[0044]FIG. 29 illustrates initial puncturing patterns for rate ⅜ TurboCodes;

[0045]FIG. 30 illustrates rate ⅜ Turbo Codes optimized at code rate ¼using frame size 512 bits;

[0046]FIG. 31 is a functional block diagram of a preferred universalconstituent encoder for rate ½ and rate ⅓ Turbo Codes of varyingInterleaver depths; and

[0047]FIG. 32 illustrates a performance comparison of rate ¼FER-optimized Turbo Codes with convolutional codes, at frame size 512bits, wherein results are consistent at 1024, 2048, and 3072 bits.

[0048] Appendix A is a compilation of figures, collectively referred toherein as ‘analogous’ figures, curves or simulations or the equivalent.

[0049] Corresponding reference characters indicate correspondingcomponents through out several views of the drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0050] The following description of the presently contemplated best modeof the invention is not to be taken in a limiting sense, but is mademerely for the purpose of describing the general principles of theinvention. The scope of the invention should be determined withreference to the claims.

[0051] There are at least two primary aspects of the currentinvention: 1) forward error correction schemes for data services basedon specific ‘universal’ Turbo Codes demonstrated to provide near optimalperformance over a wide range of information block sizes and code rates;and 2) the method by which specific Turbo Codes having the abovementioned desirable properties can be designed.

[0052] Turbo Codes are particularly well-suited to data applicationsbecause of their excellent error correction capabilities at lowsignal-to-noise (SNR) ratios and their flexibility in trading off BERand frame error rate (FER) performance for processing delay. The dataservices under consideration in the hereinafter-described embodimentsare consistent with third generation Code Division Multiple Access(CDMA) cellular mobile radio standards currently in development and aretypically more delay-tolerant than low-rate voice services.

[0053] The universal Turbo Codes specified herein (and the method offinding such codes), however, are also applicable to data services inother cellular mobile radio systems (e.g., the European Time-DivisionMultiple Access (TDMA) standard used in GSM) as well as other systems,such as satellite or other wireless communications systems. Severalspecific Turbo Codes are therefore identified that provide differentoptimizations regarding these requirements. Others would also bepossible.

[0054] In order to optimize the performance of Turbo Codes for dataservices, it is desirable to have a set of “universal” constituent codesthat provide optimal or nearly optimal performance in conjunction with avariety of different Interleaver depths and Turbo Code rates, thusavoiding tailoring each optimization of particular Turbo Codes.

[0055] Referring first to FIG. 1, an exemplary conventional digitalcellular mobile radio system using Direct Sequence Code DivisionMultiple Access (CDMA) Mobile-station-to-base-station (or reverse) linkis shown using a convolutional encoder and a Viterbi decoder. This basiccoding and interleaving can be applied, equally well, to other multipleaccess systems such as the Time Division Multiple Access (TDMA) used ina well-known GSM standard.

[0056]FIG. 1 also represents a base-station-to-mobile-station (orforward) link in a cellular mobile radio system. At a transmittingsystem 100, the system comprises a segmentation processor 104 where userinformation bits from a data terminal equipment (not shown) areassembled into fixed length frames of N bits per frame 106 which areinput to a convolutional encoder 108, (of rate r). Convolutional encoder108 is coupled to the synchronization and framing processor 104 whichproduces N/r code symbols 110 at an input of a Channel Interleaver 112coupled to the convolutional encoder 108. The channel interleaver 112,performs pseudo-random shuffling of code symbols 110, and outputs thesymbols to a Spread Spectrum modulator 114 coupled to the channelinterleaver 112. The Spread Spectrum modulator 114 uses a user specificTransmit PN-code generated by a PN converter 116 coupled to the SpreadSpectrum modulator 114, to produce a spread spectrum signal carried on aRF carrier to a mobile RF transmitter 118. Mobile RF transmitter 118 isalso coupled to the Spread Spectrum modulator 114, where a high poweramplifier (not shown) coupled to a transmit antenna 120 radiates asignal to a base station. The techniques of spread spectrum modulationand RF transmission are well known art to one familiar with spreadspectrum communication systems.

[0057] A signal from a mobile station (‘mobile signal’) received at abase station Receive antenna 122 is amplified in a Base RF receiver 124and demodulated in a Spread Spectrum Demodulator 128, using the samePN-code used by the mobile RF transmitter 118, to de-spread the signal.The demodulated symbols are de-interleaved by a Channel De-Interleaver130 and input to a Viterbi decoder 132. The decoded information bits arereconstructed into receive data blocks 136 and forwarded to the dataterminal equipment at the receive end of the system.

[0058] Referring next to FIG. 2, a hardware system for a digitalcellular mobile radio system is shown which implements an embodiment ofthe present invention. As before, a reverse link is illustrated althoughthe same block diagram also represents a forward link. Further, whilethe CDMA system is used as an example, one familiar with the art wouldconsider the present invention applicable to other systems such as TDMAas well.

[0059] Transmit data Blocks 202 from data terminal equipment aresegmented and framed at a Segmentation Processor 204 into fixed framelengths and applied to a Turbo Code encoder 208. The output from theencoder 208 is fed to a Channel Interleaver 212 to pseudo-randomize thecode symbols. The Channel Interleaver 212 provides output to a SpreadSpectrum Modulator 214 which uses a user specific PN-code from a PNGenerator 216 to create a spread spectrum signal, carried on a RFcarrier to a mobile RF transmitter 218. The channel interleaver 212 isdistinguished from a turbo code interleaver (not shown), which is acomponent of the encoder 208. The mobile RF Transmitter 218 coupled to aTransmit Antenna 220 uses a high power amplifier (not shown) at theTransmit Antenna 220 to radiate the signal to the base station.

[0060] A signal from the mobile station received at a base receiveantenna is amplified in a base RF receiver 224 and demodulated in aSpread Spectrum Demodulator 228, which uses the same PN-code as used bythe mobile RF transmitter 218, to de-spread the signal. The demodulatedsymbols are de-interleaved by the Channel DE-Interleaver 230, and inputto the Turbo Code decoder 232. Decoded information bits from the TurboCode decoder 232 are reconstructed at a Reconstruction Processor 238into receive data blocks 236 and forwarded to the data terminalequipment at the receive end.

[0061] Referring to FIG. 3, the basic structure of a Turbo Code ischaracterized by the parallel concatenation of two simpler constituentcodes at encoder #1 306 and encoder #2 308. Both constituent encoders,i.e., encoder #1 306 and encoder #2 308 process the same information bitstream 302, but the encoder #2 308 processes information bits 302 in adifferent order than the order in which encoder #1 306 processes theinformation bits 302, since the Interleaver 304 reorders the informationbits in a pseudo-random manner before they reach encoder #2 308 (theconstituent encoder 308). This arrangement reduces the likelihood that asequence of information bits 302 causing encoder #1 306 to produce alow-Hamming weight output 310 would also cause encoder #2 308 to do thesame with its output 314, which makes possible the excellent performanceof Turbo Codes.

[0062] Both encoders 306, 308 produce, in addition to the informationbits 302 (also referred to as systematic bits 302), parity bits 310, 314which are punctured by puncturer 312 to achieve a desired overall TurboCode rate. It is also possible to puncture systematic bits.

[0063] The constituent codes of a Turbo Code are usually systematic,recursive convolutional codes. The simplest and most widely knownrecursive convolutional codes have rate ½ and transfer function:

G(D)=[1,n(D)/d(D)]

[0064] where n(D) and d(D) are binary polynomials specifying the feedforward and feedback connections of the encoder, respectively.

[0065] The rate of a Turbo Code is changed by changing the selection ofoutput bits 310, 314 for puncturing or transmitting. In all the casesherein, a “1” indicates transmitting; a “0” indicates puncturing.

[0066]FIG. 3 also shows how two possible puncturing patterns result frompuncturer 312. Alternately puncturing the parity bits between encoder306 and 308 result in a Turbo Code rate r=½. Transmitting all of theparity bits at the two encoders 306, 308 produces a code rate r=⅓.

[0067] It is not possible to achieve Turbo Code rates lower than ⅓without either increasing the number of constituent encoders orincreasing the number of output parity bits per constituent encoder. Thelatter is usually preferred in order to reduce implementationcomplexity. In this case, one considers a rate ⅓ systematic, recursiveconvolutional code with transfer function:

G(D)=[1,n ₁(D)/d(D),n₂(D)/d(D)]

[0068] Using two such constituent codes provides any Turbo Code ratebetween ⅕ and 1 through puncturing, or deleting.

[0069] Turbo Codes are decoded using iterative decoding methods, asshown in the block diagram of FIG. 4.

[0070] Each of the constituent codes are decoded separately usinglikelihood estimates of the other constituent decoder 406 or 416 as ‘apriori’ information. The constituent decoder 406, 416 must be of asoft-input/soft-output type, such as the Maximum A Posteriori (MAP)algorithm, the sub-optimal Soft-Output Viterbi Algorithm (SOVA), orvariations. After both constituent decoders have processed the data, theprocess can be repeated.

[0071] In practice, the turbo decoders 406, 416 are usually limited to afixed number of iterations consistent with the implementation complexityand performance objectives of the system.

[0072]FIG. 4 is a general block diagram of a turbo decoder. Softinformation regarding the information bits 404, parity bits for thefirst encoder 402, and parity bits of the second encoder 402′ arereceived from the demodulator. First, a first decoder 406 uses receivedinformation bits 404 and received parity bits 402 to produce a softdecision 408 on information bits. The soft decision 408 is interleavedby an interleaver 412, the output of which is soft decision 414. Softdecision 414 is fed to a second decoder 416 as a priori information.

[0073] The second decoder 416 accepts the soft decision 414 describedabove and produces an improved soft decision 420 on information bitswhich are then interleaved by an interleaver 422 and fed to the firstdecoder 406 as a priori information. The whole process is repeated asmany times as desired. Final output 420 is obtained by making harddecisions or the soft decisions out of the first or second decoder.

[0074] In accordance with the present invention, a single mother TurboCode and various puncturing patterns are sought to derive uniformly goodcodes for various code rates and information block sizes.

[0075] A methodology for determining universal constituent codes isdeveloped by first limiting the initial pool of possible universalconstituent codes in accordance with trade-off studies betweenperformance and implementation complexity. In accordance with thepresent invention, performance studies using different state codes haveshown that eight-state constituent codes provide a good performancetrade-off.

[0076] Universal constituent codes are first optimized according to theprimary code rate of the targeted application. For example, in the caseof CDMA data communications, separate optimizations can be done for theforward and reverse links since the reverse links usually require lowercode rates for higher coding gain.

[0077] The following steps, more fully described below, are used toproduce Turbo Codes optimized for rate ½ and rate ⅓:

[0078] 1) select candidate systematic rate ½ constituent encoders withtransfer function of the form [1, n(D)/d(d)], where d(D) is a primitivepolynomial and n(D) starts with 1 and ends with D³;

[0079] 2) determine a Turbo Code rate ½ and rate ⅓ test puncturingpattern to apply to output data encoded by two rate ½ constituentencoders;

[0080] 3) form all possible rate ½ and rate ⅓ Turbo Codes by combiningeach rate ½ constituent code pair with the test patterns;

[0081] 4) evaluate a relative BER performance of all possible rate ½ andrate ⅓ Turbo Codes at a fixed Interleaver length;

[0082] 5) select from the group of mother pairs, a subgroup of candidatepairs for building optimized Turbo Codes based upon a best overall BERperformance;

[0083] 6) evaluate another relative BER performance of a Turbo Codegroup comprising the subgroup of candidate pairs punctured with the rate½ and rate ⅓ puncturing patterns at a plurality of other Interleaverdepths;

[0084] 7) select from the Turbo Code group, a universal code pair whichhas another best overall relative BER for the Interleaver depths; and

[0085] 8) encode data with a rate ½ or rate ⅓ Turbo Code comprising theselected universal code pair, at a first and a second encoder, theencoders similar and an Interleaver feeding bits into the secondencoder, wherein the bits are ordered differently before entering eachencoder.

[0086] Once generated, best Turbo Codes of lower rates such as ¼, whichare compatible with the rate ½ and ⅓ Turbo Codes determined by the abovesteps, can also be determined.

[0087] Rate ½ Constituent Codes

[0088] The following describes how rate ½ constituent codes aredetermined in one embodiment.

[0089] First, a list of candidate eight-state, rate ½ constituent codepolynomials are determined.

[0090] Table 1 lists the determined denominator polynomials d(D) andnumerator polynomials n(D) in octal notation. There are twelveconstituent code candidates considered for initial screening purposes.TABLE 1 Candidate 8-State Constituent Encoders of Rate ½ DenominatorPolynomial Numerator Polynomial d (D) n (D) (octal notation) (octalnotation) 11 13 11 15 11 17 13 11 13 15 13 17 15 11 15 13 15 17 17 11 1713 17 15

[0091] Each of the twelve (12) polynomials is expressed in octal form inTable 1, and has a corresponding binary and polynomial notation. Thebinary equivalent, for example of octal 13, is binary 1011. Binary 1011corresponds to a polynomial d(D)=D⁰(1)+D¹(0)+D²(1)+D³(1)+D²+D³.

[0092] Next, the candidate Turbo Codes are simulated with an interleaversize of 1000 bits and three decoder iterations. The preliminaryscreening, which results are shown in FIG. 5 and FIG. 6, evaluates theBit Error Rate (BER) versus Ebi/No performance of all candidate TurboCodes of rate ½ and rate ⅓, as described above. Measurement of Ebi/No isequivalent to a relative SNR.

[0093] The results of FIG. 5 and FIG. 6 are used to select six (6) codepolynomial pairs. The six (6) candidate universal code pairs, d(D)-n(D),are shown in octal representation on the left hand side of Table 2below.

[0094] Next, a corresponding performance of the eight-state Turbo Codes,using simulated data with the candidate universal codes at each rate andInterleaver depth, is used to construct Table 2. A sample performancestudy or simulation is shown in FIGS. 7 and 8 showing selected TurboCodes at an Interleaver depth of 512 bits for rate ½ and rate ⅓.

[0095] Table 2 below shows the approximate SNR loss for simulated datadue to using a non-optimized code at rates ½ and ⅓ and Interleaverdepths of 512, 1024, 2048, and 3072 bits. TABLE 2 Approximate SNR Lossdue to Use of Non-Optimized Codes Candidate Universal Turbo Code Rate &Frame Size (bits) Code: ½ & ½ & ½ & ½ & ⅓ & ⅓ & ⅓ & ⅓ & d(D)-n(D) 5121024 2048 3072 512 1024 2048 3072 15-13 0.005 0.00 0.00 0.05 0.10 0.050.05 0.10 dB dB dB dB dB dB dB dB 13-15 0.00  0.00 0.00 0.00 0.05 0.050.05 0.05 dB dB dB dB dB dB dB 15-17 0.05  0.05 0.00 0.05 0.05 0.05 0.000.10 dB dB dB dB dB dB dB dB 17-15 0.40  0.50 0.00 0.00 0.05 0.00 dB dBdB dB dB dB 17-13 0.40  0.50 0.00 0.00 0.00 0.00 dB dB dB dB dB dB 13-170.05  0.05 0.05 0.00 0.00 0.10 0.00 0.10 dB dB dB dB dB dB dB dB

[0096] In a similar simulation using sixteen-state codes, pairs denotedas 31-33 and 31-27 are also shown in sample FIGS. 7 and 8 using four (4)decoder iterations for each sixteen-state code in order to providesimilar complexity comparison with the eight-state codes using eight (8)decoder iterations. Eight-state codes with eight iterations out-performsixteen state codes with four iterations significantly.

[0097] With separate simulations, the difference in performance amongstthe different interleavers using the above six (6) candidate pairs isobserved to be within 0.05 dB.

[0098] Finally, the results of Table 2 show that the following rate ½constituent code pair provides the best overall performance across theranges of rates and Interleaver sizes studied:

d(D)=1+D ² +D ³ ;n(D)=1+D+D ³

[0099] which represents octal 13 and octal 15, respectively.

[0100] In each tabulated case, the performance of Codes 13-15 is within0.05 dB to the best performing code for that rate and Interleaver size.

[0101] This constituent code is thus selected as the basis for TurboCode designs where higher code rates such as ½ and ⅓ are dominant.

[0102] Rate ⅓ Constituent Code

[0103] The following describes how rate ⅓ constituent codes aredetermined. Similar to the rate ½ constituent codes, rate ⅓ constituentcode candidates are identified in Table 3 below for building nearoptimal Turbo Code rates of ¼ and ⅕. For this case, the constituent codecandidates for a Turbo Code must have three (3) polynomials instead oftwo (2). TABLE 3 Candidate Constituent Codes for Optimized Lower-RateTurbo Codes CC#1 CC#2 CC#3 (Octal 13-{fraction (15/17)}) (Octal15-{fraction (13/17)}) (Octal 17-{fraction (13/15)}) d(D) = 1 + D² + D³d(D) = 1 + D + D³ d(D) = 1 + D + D² + D³ (Octal 13) (Octal 15) (Octal17) n ₁(D) = 1 + D + D³ n₁(D) = 1 + D² + D³ n₁(D) = 1 + D² + D³ (Octal15) (Octal 13) (Octal 13) n₂ (D) = 1 + D + D² + D³ n₂(D) = 1 + D + D² +D³ n₂(D) = 1 + D + D³ (Octal 17) (Octal 17) (Octal 15)

[0104] Optimal Rate {fraction (1/4)} Turbo Codes

[0105] In order to build an overall rate ¼ Turbo Code, variouspuncturing schemes must be considered in combination with eachconstituent codes of Table 3.

[0106] The various puncturing schemes of FIG. 9 are first considered.For a rate ¼ code, a common input information bit or systematic bit, istransmitted by one encoder, along with three (3) of four (4) parity bitsproduced for that input bit, by the two encoders.

[0107] The puncturing patterns of FIG. 9, namely 910, 920, 930, and 940,are selected based upon the previously mentioned design principles, tomeet stipulated code rates.

[0108] Next, each of the three (3) code triads of Table 3 is combinedwith the four (4) puncturing patterns 910, 920, 930 and 940, of FIG. 9to produce twelve (12) possible Turbo Codes to be evaluated withsimulated data shown in FIGS. 10 through 12 for a fixed Interleaverdepth of 512 bits, for example.

[0109] The performance of the twelve (12) Turbo Codes above is then usedto select three (3) best Turbo Code candidates for a more detailedevaluation. Based on the simulation results shown in FIGS. 10 through12, the three (3) best Turbo Code candidates from the twelve (12) are:

[0110] 1) Turbo Code A—Constituent Code No. 1 with puncturing PatternNo. 2;

[0111] 2) Turbo Code B—Constituent Code No. 2 with puncturing PatternNo. 1; and

[0112] 3) Turbo Code C—Constituent Code No. 3 with puncturing PatternNo. 1. (Puncturing patterns are selected from FIG. 9, Patterns 910, 920,930 and 940).

[0113] One of the Turbo Codes of Codes A through C is next selected forfurther evaluation using simulated data at various additionalInterleaver frame sizes to verify that the puncturing patterns are alsogood at other Interleaver depths.

[0114] To confirm the basic methodology, the performance of a Turbo Codebased upon Constituent Code No. 1 (for example) is simulated for framesizes of 1024, 2048 and 3072 bits. Sample results for BER/FERperformance of Code #1 at 1024 bits is shown in FIG. 13 and confirms thebasic methodology.

[0115] Next, FIG. 14 shows the BER/FER performance of simulated datausing the three rate ¼ Turbo Code Candidates A through C at anInterleaver depth of 512 bits. Consistent results are also achieved atInterleaver sizes 1024, 2048 and 3072 bits.

[0116] Next, a rate ¼ Turbo Code candidate is selected from CandidateTurbo Codes A through C which provides the best overall performance atall Interleaver depths, in the simulation resulting in FIG. 14 andanalogous figures, such as those depicted in Appendix A. In the case ofthe rate ¼ Turbo Code, optimization based on BER performance gives adifferent result than optimization based on FER performance. Turbo CodeB has the best overall FER performance and Turbo Code C the best overallBER performance, for the simulated data. FIG. 15 shows the performanceof Turbo Code B as compared to other puncturing schemes.

[0117] Thus, FER optimized Turbo Code B is selected as the basis for thedesign since FER performance is usually the more important criteria fordata services. On the other hand, Turbo Code A can be punctured to givethe same universal Turbo Code identified previously as optimal for rate⅓ (by puncturing all parity bits from the n₂ (D) polynomial). Hence,Turbo Code A is the preferred choice for the forward link rate ¼ codesin order to have a single universal mother code to implement all of thedifferent code rates.

[0118] Although current third generation CDMA encoding primarilyconcerns rate ¼ channel encoding on the reverse link, rate ⅓ and rate ½channel coding may be required for some of the highest rate datachannels. A universal Turbo Code for rate ¼, rate ⅓, and rate ½ can bedesigned, wherein the underlying constituent code is the same and onlythe puncturing pattern used is different. The method for generating thehigher rate Turbo Codes from the rate ⅓ constituent code follows.

[0119] Rate ⅓ Turbo Codes Optimized at Rate ¼

[0120] Using the constituent codes derived from the rate ¼ optimizedTurbo Codes above, namely Turbo Code B, the rate ⅓ and rate ½ Turbo Codecan be designed to be compatible thereto. Thus, Constituent Code No. 2(from Code B) is used as the basis.

[0121]FIG. 16 shows seven (7) basic puncturing patterns that can be usedto produce a rate ⅓ Turbo Code and four (4) basic puncturing patterns toproduce a rate ½ Turbo Code. The seven (7) rate ⅓ patterns, 1602 through1614 in block diagram 1600, show the consecutive information puncturingbit patterns, 1620, 1626, and the four (4) corresponding row parity bitpuncturing patterns 1622, 1624, 1628, and 1630, for the two (2) encoderpuncturing block patterns 1616 and 1618. As before, the pattern “1111”shown in row 1620 always transmits all the information bits from encoder1. The pattern “0000” of row 1626, always punctures the information bitsthat enter by encoder No. 2. This is because it is not necessary totransmit the information bit twice. The four (4) rate ½ puncturingpatterns, 1 through 4, identified in FIG. 16 as element numbers 1640,1642, 1644, and 1646, follow the same notation.

[0122] Next, in FIG. 17 the BER and FER performance of all possible rate⅓ Turbo Codes simulated with the preferred Constituent Code No. 2 at anInterleaver depth of 512 bits are compared.

[0123] Then the two (2) best patterns are selected for furtherconsideration. Next, the performance of these two (2) patterns arecompared at further Interleaver depths 1024, 2048 and 3078 bits.

[0124] In FIG. 17, for example, showing the rate ⅓ puncturing patternsat 512 bits, Patterns 2 and 5 are selected based upon curves 1710 and1720, as having the best and next best overall relative FER,respectively.

[0125] Pattern 2 is then selected as the best performer over the variousInterleaver depths from further simulations analogous to that of FIG. 17at additional Interleaver sizes for 1024, 2048 and 3072 bits.

[0126] Rate ½ Turbo Codes Optimized at Rate ¼

[0127] Rate ½ Codes can also be optimized at lower rate codes forsimilar compatibility as described above. FIG. 18 compares the BER andFER simulated performance of all the rate ½ Turbo Codes at anInterleaver depth of 512 bits. FIG. 18 is generated using ConstituentCode No. 2 and the four (4) puncturing patterns shown in FIG. 16 for arate ½ Turbo Code. Patterns 1 and 4 are determined to be the best basedupon simulated curves 1810 and 1820 for FER performance.

[0128] As in the rate ⅓ case optimized at rate ¼, similar simulationcurves to FIG. 18 are done for Patterns 1 and 4 for Interleaver depthsof 1024, 2048 and 3072 bits. Based upon the resulting performance/curvesPattern 1 is judged to be the best pattern for FER performance.

[0129] Preferred Universal Turbo Codes Optimized for Rate ½ and ⅓

[0130]FIG. 19 shows a block diagram for the constituent encoderoptimized in accordance with the previously described method for TurboCode rates ½ and ⅓. FIG. 20 shows the block diagram for thecorresponding Turbo Code punctured to rate ¼.

[0131] Information bit stream X(t) 1902 is received at a switch 1922,and is processed in accordance with several modular adders 1904, 1908,1920, 1910, 1914, 1918, 1919, and several shift registers 1906, 1912 and1916 which are hard-wired to represent two (2) numerator polynomials andone denominator polynomial.

[0132] In FIG. 19, the denominator polynomial d(D), represented in octal13, is hardwired by the return feedback connection to modular adders1920 and 1904. Before computing, three shift registers 1906, 1912 and1916 are first zeroed.

[0133] A first numerator polynomial over a denominator polynomial,represented by “11101”, is hardwired to return output Y₀(t) bycombining: X(t) 1902 with a result of modulator adder 1920 to create afirst bit W(t); the modular sum (second bit) of shift register 1906 andW(t) from the modular adder 1908; another zero bit (third bit) indicatedby the lack of connection to the register 1912; and the modular sum(fourth bit) of another register 1916 and a result of modular adder 1908from modular adder 1998. The result is Y₀(t)=W(t)+S₀(t)+S₂(t).

[0134] In FIG. 19 a second numerator polynomial over a denominatorpolynomial, represented by “1111”, is hardwired to return output Y₁(t)by combining: X(t) 1902 with a result of adder 1920 to create a firstbit W(t); adding contents of a further register 1906 to W(t) with thecontents of the modular adder 1910 (second bit); adding contents of theregister 1912 a result of adder 1710 with the modular adder 1914 (thirdbit); and adding contents of the other register 1916 to a result ofadder 1914 with modular adder 1919 (fourth bit). The result isY₁(t)=W(t)+S₀(t)+S₁(t)+S₂(t).

[0135] In FIG. 19, the denominator polynomial connections sum the resultof the register 1912 with register 1916 at adder 1920 and then adds itto X(t) 1902 at adder 1904. Thus, if modular adder 1904 is the valueW(t), register 1906 holds S₀(t), register 1912 holds S₁(t) and register1916 holds S₂(t), and adder 1904 produces W(t)=X(t)+S₁(t)+S₂(t);Y₀(t)=W(t)+S₀(t)+S₂(t); and Y₁(t)=W(t)+S₀(t)+S₁(t)+S₂(t). Thus, theadding is cumulative.

[0136] The result of a modular adder is a “1” if the two bits aredifferent, and a “0” if the two bits are the same. Output Y₀(t)represents the output from numerator Polynomial No. 1 and thedenominator polynomial. Output Y₁(t) represents numerator Polynomial No.2 and denominator polynomial.

[0137] Initially, S₀=S₁=S₂=0 and the values of the registers 1906, 1912,1916 are shifted from left to right after each clock cycle increment.Thus, S₀(t+1)=W(t); S₁ (t+1)=S₀(t), and S₂(t+1)=S₁(t).

[0138] The optimal puncturing matrices, shown in FIG. 20, for example,show a “1” for transmitted bits and a “0” for punctured bits. ExemplaryFIG. 20 shows encoder 2000 with incoming bit X(t) and Interleaver 2002passing interleaved bits X′(t) to encoder 2006 to produce output bitX′(t) and parity bits Y₀ ¹(t), and Y₁ ¹(t). None of the interleaved bitsx′(t) are processed in the rate ¼ encoder 2004, only in the second rate¼ encoder 2006. Block 2010 shows the puncturing pattern matrices.

[0139] More complicated puncturing patterns can be used to achieve otherpossible coding rates. For example, it is possible to select optimalpuncturing patterns to achieve rates ⅜ and {fraction (4/9)} for TurboCodes optimized at rates ½ and ⅓; and to achieve rates {fraction (2/9)}and ⅜ for Turbo Codes optimized at rate ¼ using the preferred TurboCodes identified in the invention.

[0140] Similar to FIG. 9 the blockdiagram for an optimal Turbo Code rate⅜ uses the rate ⅓ mother constituent code of FIG. 20. The encoder forthe constituent code of FIG. 20 is shown in FIG. 19. The puncturingpattern of the rate ⅜ Turbo Codes shown in FIG. 21 punctures 1 out ofevery 6 bits associated with the first numerator polynomial from bothencoders to generate a rate ⅜ Turbo Code.

[0141] The second pattern is a extension of the first pattern allowingboth constituent encoders to have the same rate, namely {fraction(6/11)}. The extension pattern duplicates the same pattern (matrix) foranother three (3) bits but moves the location of one transmission bitfrom one encoder to another, essentially flipping a “1” in one encoderwhile flipping a “0” in another encoder at the analogous locations.

[0142]FIG. 22 shows the performance of these patterns at an Interleaverdepth of 512 bits. Based on these and analogous curves at 1024, 2048,and 3072 Interleaver depths, Pattern 2 is chosen to implement the rate ⅜Turbo Codes.

[0143]FIG. 23 shows the puncturing patterns selected for rate {fraction(4/9)} Turbo Codes used with the mother of codes of FIG. 20. Similarly,the second pattern is an extension of the first, which allows bothconstituent encodes to have the same rate, namely {fraction (8/13)}.

[0144]FIG. 24 shows the corresponding performance curves. Pattern 2 ischosen to implement the rate {fraction (4/9)} Turbo Codes.

[0145] Thus, one exemplary Turbo Code design, optimized for Turbo Coderates ½ and ⅓, and universal for all Interleaver depths, has thepreferred generator polynomials d(D)=1+D²+D³, n₁ (D)=1+D+D³, andn₂(D)=1+D+D²+D³.

[0146] The preferred puncturing patterns for various code rates are:

[0147] 1) Rate ¼—alternately puncturing parity bits n₁ from one encoderand n₂ from the same encoder;

[0148] 2) Rate ⅓—puncturing parity bits n₂ from both encoders;

[0149] 3) Rate ½—puncturing parity bits n₂ and alternately puncturingparity bits n₁ from both encoders;

[0150] 4) Rate ⅜—puncturing parity bits n₂ and one out of every 6 paritybits n₁ from both encoders; and

[0151] 5) Rate {fraction (4/9)}—puncture parity bits n₂ and uniformly 3out of every 8 parity bits n₁ from both encoders.

[0152] A simplified version of this code is the universal Turbo Codedesign consisting of two constituent encoders having generatorpolynomials d(D)=1+D₂+D₃ and n₁(D)=1+D+D³. (The third polynomial n₂(D)is not used, so the corresponding output is not generated and theencoder block diagram is simplified by removing the correspondingconnections.) This universal Turbo Code design supports a minimum coderate equal to ⅓ (instead of ⅕). The corresponding preferred set ofpuncturing patterns are:

[0153] 1) Rate ⅓—no puncturing

[0154] 2) Rate ½—alternately puncturing parity bits n₁ from bothencoders;

[0155] 3) Rate ⅜—puncturing one out of every 6 parity bits n₁ from bothencoders; and

[0156] 4) Rate {fraction (4/9)}—puncturing uniformly 3 out of every 8parity bits n₁ from both encoders.

[0157] Preferred Universal Turbo Codes Optimized for Code Rate ¼

[0158] The basic block diagram for a preferred constituent encoder isshown in FIG. 25.

[0159]FIG. 26 is an encoder block diagram for the preferred rate ¼ TurboCode. In this case, the second parity bits are alternately punctured bythe two constituent encoders. The preferred puncturing patternsdescribed in earlier section can then be applied to produce rate ⅓ andrate ½ Turbo Codes. Other rates can also be supported by identifyingfurther puncturing patterns. This is illustrated by considering rates{fraction (2/9)} and ⅜.

[0160]FIG. 27 shows the puncturing patterns for a rate {fraction (2/9)}Turbo Code. Three (3) different patterns are compared by performancecurves in FIG. 28 and analogous curves, such as those set forth, forexample, in Appendix A, showing performance at various frame Interleaversizes. From a Pattern 2 FER curve 2810 and analogous curves, Pattern No.2 is chosen as the optimal FER pattern for rate {fraction (2/9)}.

[0161] Next, FIG. 29 illustrates six (6) initial screening puncturingpatterns for optimizing a rate ⅜ Turbo Code. The performance of thesepatterns is simulated at a fixed Interleaver depth of 512 bits. Based onthe simulation, Pattern 5 and Pattern 6 are chosen as the optimalpuncturing patterns for further review.

[0162] Two more extension Patterns 7 and 8 of the above Patterns 5 and 6duplicate the same patterns for another three information bits, but movethe location of one of the transmission bits in the parity sequence fromone encoder pattern to another. The extension allows both constituentencoders to have the same rate, namely {fraction (6/11)} at eachencoder.

[0163]FIG. 30 shows exemplary performance curves of the above four (4)candidate puncturing Patterns 5, 6, 7 and 8 for rate ⅜ turbo Codes.Based on these results, a Pattern 8 FER curve 3010 and analogous curvessuch as those shown, for example, in Appendix A, demonstrate thatPattern 8 is the optimal puncturing pattern for rate ⅜ Turbo Codes.

[0164] Thus, one preferred Universal Turbo Code design optimized forRate ¼ uses two constituent codes having polynomials d(D)=1+D+D³,n₁=1+D²+D³ and n₂=1+D+D²+D³.

[0165] The below puncturing patterns are associated optimized patternsas previously discussed for Turbo Code rate ¼ and FER performance formost commonly used Turbo Code rates, where n₁ represents output bitsassociated with a first numerator polynomial, and n₂ represents outputbits associated with a second numerator polynomial:

[0166] 1) Rate ¼—alternately puncture parity bits n₂ from bothconstituent encoders.

[0167] 2) Rate ⅓—puncture parity bits n₁ from both constituent encoders;

[0168] 3) Rate ½—puncture parity bits n₂ and every other parity bits n₁from both encoders;

[0169] 4) Rate {fraction (2/9)}—puncture every one out of every fourparity bits in n₁ from both encoders; and

[0170] 5) Rate ⅜—puncture parity bits n₁ and one out of every six paritybits n₂.

[0171] These preferred puncturing patterns can also be cyclicallyshifted without affecting performance. The cyclically shifted patternsare equivalent.

[0172] Turbo Coding FEC Schemes for CDMA Data Services

[0173] The set of preferred universal Turbo Codes described heretoforein this invention provide a suite of flexible high performance channelcodes that are well suited for sophisticated data communication systemsrequiring a variety of low speed and high speed data services. Thissuite of preferred universal Turbo Codes allows the crafting ofdifferent Turbo encoding schemes to meet the specific requirements ofparticular data communication systems.

[0174] As a first example, either of the following two FEC schemes iswell-suited and recommended for a synchronous CDMA data communicationsnetwork (such as the third generation CDMA 2000 system currently underdevelopment):

[0175] 1) The preferred universal Turbo Code optimized at codes rates ½and ⅓, along with a subset of associated preferred puncturing patterns,on a forward link; and the preferred universal Turbo Code optimized atcode rate ¼, along with a subset of the associated preferred puncturingpatterns, on a reverse link; and

[0176] 2) The preferred universal Turbo Code optimized at codes rates ½and ⅓, along with a subset of associated preferred puncturing patterns,on both the forward and reverse links.

[0177] As a second example, either of the following FEC schemes iswell-suited and recommended for an asynchronous CDMA data communicationsnetwork (such as the third generation CDMA systems currently indevelopment in Europe and Asia):

[0178] 1) The preferred universal Turbo Code optimized at code rates ½and ⅓, described above, along with a subset of associated puncturingpatterns, on both the forward and reverse links;

[0179] 2) The preferred universal Turbo Code optimized at code rate ¼,described above, along with a subset of the associated preferredpuncturing patterns, on both the forward and reverse links; and

[0180] 3) The simplified version of the universal Turbo Code, describedabove, along with a subset of the associated preferred puncturingpatterns, on both the forward and reverse links.

[0181] The choice of which option to implement depends on the expecteddominant code rate, minimum code rate, and implementation complexityconstraints as well as other system requirements. Of course, additionalpuncturing patterns could be designed in accordance with the teachingsof this invention to provide other Turbo Coding rates.

[0182] Other Variations

[0183] The universal Turbo Codes identified for high-speed data servicesare especially suitable for third generation CDMA cellular mobile radiosystems but could be easily applied to other systems as well.

[0184] Well known variations such as Frame Oriented Convolutional TurboCoding (FOCTC) could also be used in conjunction with the preferreduniversal constituent codes and universal Turbo Codes of this invention.The design methodology for selecting universal constituent codes anduniversal Turbo Codes can also be applied to alternate Turbo Codestructures such as those involving more than two constituent encoders,and those involving serial concatenation instead of or in addition toparallel concatenation.

[0185] The exemplary preferred puncturing patterns described herein canbe refined or modified in various ways by those skilled in the art. Forexample, a cyclic shift of a preferred puncturing pattern offerssubstantially equivalent performance as the preferred puncturing patterndescribed herein. Furthermore, specific data communication systems mayrequire different and additional puncturing patterns to support ratematching. These puncturing patterns may be designed in accordance withthe teachings of the present invention.

[0186] While the invention herein disclosed has been described by meansof specific embodiments and applications thereof numerous modificationsin variations could be made thereto by a skilled artisan and withoutdeparting from the scope of the invention set forth in the claims.

What is claimed is:
 1. The method of providing forward error correctionfor data services using a parallel concatenated convolutional code whichis a Turbo Code comprising of a plurality of eight-state constituentencoders wherein a plurality of data block sizes are used in conjunctionwith said Turbo Code.
 2. The method of claim 1 wherein at least one ofthe plurality of eight-state constituent codes has a transfer functionequal to G(D)=[1,(1+D+D³)/(1+D²+D³)].
 3. The method of claim 2 whereinthe Turbo Code comprises two constituent codes, the Turbo Code enablinga minimum code rate equal to ⅓.
 4. The method of claim 3 wherein aplurality of code rates greater than or equal to ⅓ are provided by theTurbo Code by puncturing one or more output coded bits from the twoconstituent encoders.
 5. The method of claim 1 wherein at least one ofthe plurality of eight-state constituent codes has a transfer functionG(D)=[1,(1+D+D³)/(1+D²+D³), (1+D+D²+D³)/(1+D²+D³)].
 6. The method ofclaim 5 wherein the Turbo Code consists of two constituent codes, theTurbo Code enabling a minimum code rate equal to ⅕.
 7. The method ofclaim 6 wherein a plurality of code rates greater than or equal to ⅕ areprovided by the Turbo Code by puncturing one or more output coded bitsfrom the two constituent encoders.
 8. The method of claim 1 wherein atleast one of the plurality of eight-state constituent codes has atransfer function G(D)=[1,(1+D²+D³)/(1+D+D³)].
 9. The method of claim 8wherein the Turbo Code comprises two constituent codes, the Turbo Codeenabling a minimum code rate equal to ⅓.
 10. The method of claim 9wherein a plurality of code rates greater than or equal to ⅓ areprovided by the Turbo Code by puncturing one or more output coded bitsfrom the two constituent encoders.
 11. The method of claim 10 whereinthe Turbo Code consists of two constituent codes, the Turbo Codeenabling a minimum code rate equal to ⅕.
 12. The method of claim 11wherein a plurality of code rates greater than or equal to ⅕ areprovided by the Turbo Code by puncturing one or more output coded bitsfrom the two constituent encoders.
 13. The method of claim 1 wherein atleast one of the plurality of eight-state constituent codes has atransfer function G(D)=[1,(1+D²+D³)/(1+D+D³), (1+D+D²+D³)/(1+D+D³)].